Classes of general \(H\)-matrices (Q952030)

Three classes of \(H\)-matrices \(A \in \mathbb C ^{ n \times n}\), one of them with non-singular and the other two with singular comparison \(M\)-matrices \({\mathcal M}(A)\) are examined. In the third mixed class there are both singular and non-singular matrices in the set of equimodular matrices of \(A\). Necessary or sufficient conditions are obtained to conclude as to whether a given \(A\) is an \(H\)-matrix, and if so, to which class in question it belongs. A classification of the \(H\)-matrices considered then follows.